Label Class Class size Class degree Base field Field degree Field signature Conductor Conductor norm Discriminant norm Root analytic conductor Bad primes Rank Torsion CM CM Sato-Tate $\Q$-curve Base change Semistable Potentially good Nonmax $\ell$ mod-$\ell$ images $Ш_{\textrm{an}}$ Tamagawa Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
1083.2-b5 1083.2-b $6$
$8$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
1083.2
\( 3 \cdot 19^{2} \)
\( 3^{4} \cdot 19^{4} \)
$0.88788$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$3.264688998$
0.942434535
\( \frac{30664297}{3249} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-7{x}+5$
61731.2-b4 61731.2-b $6$
$8$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
61731.2
\( 3^{2} \cdot 19^{3} \)
\( 3^{10} \cdot 19^{10} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{5} \)
$1$
$0.432418621$
0.998628029
\( \frac{30664297}{3249} \)
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -313 a + 410\) , \( 979 a + 1998\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-313a+410\right){x}+979a+1998$
61731.3-b4 61731.3-b $6$
$8$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
61731.3
\( 3^{2} \cdot 19^{3} \)
\( 3^{10} \cdot 19^{10} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{5} \)
$1$
$0.432418621$
0.998628029
\( \frac{30664297}{3249} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 97 a - 410\) , \( -980 a + 2978\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(97a-410\right){x}-980a+2978$
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Pari/GP
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
